This note investigates the distributed estimation problem for continuous-time linear time-invariant (LTI) systems observed by a network of observers. Our starting point is a given LTI system whose full state vector we want to estimate, based on the measured output of the system. We will call this the observed system. Each observer in the network has access to only part of the output of the observed system, and communicates with its neighbors according to a given network graph. In this note we recover the known result that if the observed system is observable and the network graph is a strongly connected digraph, then a distributed observer exists. Moreover, the estimation error can be made to converge to zero at any a priori given decay rate. Our approach leads to a relatively straightforward proof of this result, using the mirror of the balanced graph associated with the original network graph. The numerical design of our distributed observer is reduced to solving linear matrix inequalities (LMI's). Each observer in the network has state dimension equal to that of the observed plant.

This paper investigates interval estimation methods for discrete-time linear time-invariant systems. We propose a novel interval estimation method by integrating robust observer design with reachability analysis. By introducing $H_\infty$ design into interval estimation, the proposed method is effective in improving the accuracy of interval estimation. Moreover, the comparisons and relationships between the existing methods and the proposed method are discussed in detail. Finally, simulation results are presented to demonstrate the effectiveness of the proposed method.

This paper proposes a novel interval observer design method for discrete-time Takagi-Sugeno fuzzy systems with parametric uncertainty, disturbances, and measurement noise. We present a new structure of interval observer with more design parameters, which can be used to broaden the application scope of interval observer design. For improving the accuracy of interval estimation, an L _∞ norm-based approach is used in the design of interval observer to attenuate the effect of the unknown disturbances, noise, and parametric uncertainty. Furthermore, the design conditions are formulated into a set of linear matrix inequalities, which can be efficiently solved. Numerical simulations are given to illustrate the effectiveness of the proposed method.

This article deals with the problem of fault detection for discrete-time Lipschitz nonlinear systems subject to a class of restricted frequency-domain specifications. We present a novel observer structure with more design parameters, which can be applied to enhance the observer performance. The performances of fault sensitivity and disturbance robustness are characterized using finite-frequency $H_{-}$ and $H_{\infty }$ indices, respectively. Less restrictive design conditions are obtained based on a reformulated Lipschitz property. Moreover, to detect faults timely, a novel dynamic threshold is synthesized based on zonotopic set-membership techniques. Simulation examples are conducted to demonstrate the viability and validity of the presented method.